Debugging the Quantum Physics Sequence
This article should really be called “Patching the argumentative flaw in the Sequences created by the Quantum Physics Sequence”.
There’s only one big thing wrong with that Sequence: the central factual claim is wrong. I don’t mean the claim that the Many Worlds interpretation is correct; I mean the claim that the Many Worlds interpretation is obviously correct. I don’t agree with the ontological claim either, but I especially don’t agree with the epistemological claim. It’s a strawman which reduces the quantum debate to Everett versus Bohr—well, it’s not really Bohr, since Bohr didn’t believe wavefunctions were physical entities. Everett versus Collapse, then.
I’ve complained about this from the beginning, simply because I’ve also studied the topic and profoundly disagree with Eliezer’s assessment. What I would like to see discussed on this occasion is not the physics, but rather how to patch the arguments in the Sequences that depend on this wrong sub-argument. To my eyes, this is a highly visible flaw, but it’s not a deep one. It’s a detail, a bug. Surely it affects nothing of substance.
However, before I proceed, I’d better back up my criticism. So: consider the existence of single-world retrocausal interpretations of quantum mechanics, such as John Cramer’s transactional interpretation, which is descended from Wheeler-Feynman absorber theory. There are no superpositions, only causal chains running forward in time and backward in time. The calculus of complex-valued probability amplitudes is supposed to arise from this.
The existence of the retrocausal tradition already shows that the debate has been represented incorrectly; it should at least be Everett versus Bohr versus Cramer. I would also argue that when you look at the details, many-worlds has no discernible edge over single-world retrocausality:
Relativity isn’t an issue for the transactional interpretation: causality forwards and causality backwards are both local, it’s the existence of loops in time which create the appearance of nonlocality.
Retrocausal interpretations don’t have an exact derivation of the Born rule, but neither does many-worlds.
Many-worlds finds hope of such a derivation in a property of the quantum formalism: the resemblance of density matrix entries to probabilities. But single-world retrocausality finds such hope too: the Born probabilities can be obtained from the product of ψ with ψ*, its complex conjugate, and ψ* is the time reverse of ψ.
Loops in time just fundamentally bug some people, but splitting worlds have the same effect on others.
I am not especially an advocate of retrocausal interpretations. They are among the possibilities; they deserve consideration and they get it. Retrocausality may or may not be an element of the real explanation of why quantum mechanics works. Progress towards the discovery of the truth requires exploration on many fronts, that’s happening, we’ll get there eventually. I have focused on retrocausal interpretations here just because they offer the clearest evidence that the big picture offered by the Sequence is wrong.
It’s hopeless to suggest rewriting the Sequence, I don’t think that would be a good use of anyone’s time. But what I would like to have, is a clear idea of the role that “the winner is … Many Worlds!” plays in the overall flow of argument, in the great meta-sequence that is Less Wrong’s foundational text; and I would also like to have a clear idea of how to patch the argument, so that it routes around this flaw.
In the wiki, it states that “Cleaning up the old confusion about QM is used to introduce basic issues in rationality (such as the technical version of Occam’s Razor), epistemology, reductionism, naturalism, and philosophy of science.” So there we have it—a synopsis of the function that this Sequence is supposed to perform. Perhaps we need a working group that will identify each of the individual arguments, and come up with a substitute for each one.
It’s worth noting that Mitchell Porter’s true objection to Many-Worlds is (if I recall correctly) his conviction that quantum phenomena are at the root of human consciousness and qualia, and that this would be ruined in the Everett interpretation.
I don’t think that’s very relevant in this context. There are other people who aren’t enamored with the section on MWI in the sequences, for reasons including those Mitchell outlines here.
He very carefully wrote this post to avoid his real objections and instead come across as a neutral-point-of-view expert. I found this disingenuous, and I think that the context might be especially helpful to readers who haven’t been around for all that long.
I wrote the post in order to get a hole in the logic of the Sequences fixed. And the argument I presented was chosen in order to be as simple and convincing as possible: the existence of a whole class of interpretations that are unaddressed in the Sequence, and which exist at approximately the same level of qualitative plausibility as many worlds, when judged by the pre-Copenhagen standards of mathematical physics.
You’re also wrong about my “real objections”, in two ways. The way you put it was that I want consciousness to be explained by something quantum, and MWI kills this hope. But in fact my proposition is that consciousness is based on entanglement—on a large tensor factor of the quantum state of the brain. MWI has no bearing on that! MWI is entanglement-friendly. If some other version of quantum theory says there’s entanglement in the brain, that entanglement will still be present in many-worlds. (Retrocausal theory is actually much less entanglement-friendly, because it generally doesn’t believe in wavefunctions as physical objects.) My philosophy-of-mind objections to MWI-based theories of personhood have to do with MWI tolerance of vagueness regarding when one person becomes two, and skepticism that a branching stream of consciousness is even logically possible.
But more importantly, the other criticisms of MWI that I make are just as “real”. I really do consider a large fraction of what is written in support of MWI, to be badly thought out, describing ideas which aren’t a physical theory in any rigorous sense. I really do think that the only reasonable way to explain the Born probabilities is to exhibit a multiverse in which those are the actual frequencies of events, and that this is not the case for 99% of what is written about MWI. I really do think that the problem posed for MWI by relativity is not properly appreciated.
Despite all this, I’m willing to engage with MWI a little because it still has some microscopic chance of being true, and also because it does have roots in the formalism. I believe the way to the answer does not just involve pluralism of research, but active hybridization of interpretations, especially at their points of contact with the mathematical theory.
If I understand their thinking correctly, people who believe in MWI think decoherence is responsible for the difference between one copy of a person and their almost-duplicate in another branch. So quantum mechanics turns out to play an absolutely fundamental role in any MWI-based account of consciousness, too; and I certainly have objections to the philosophy of identity that results.
But I’ve always had multiple problems with MWI, even when judging it just by standards appropriate to mathematical physics. Perhaps the majority of MWI advocacy consists of nothing but rhetoric—adopting the stance that “the wavefunction is all there is, and it doesn’t collapse”. Many exponents of MWI seem to have trouble understanding that relativity and the Born rule pose specific technical challenges to this assertion, and that they must ultimately present an implementation (of relativity) or derivation (of the Born rule) that is endogenous to the no-collapse framework; otherwise, they don’t truly have a physical theory.
I find it remarkable that after years of reading about this stuff, the very first time I have seen even the beginning of a satisfactory approach to relativistic MWI is to be found in an obscure comment on an Internet physics forum (see the section called “Semi-local classical illustration”), dating from earlier this year. To me, that says something about the quality of the discourse about MWI—that the problem of relativity has hardly been posed or tackled. MWI fans may disagree with this, they may think that relativity has been given appropriate attention in the past; but my point is that these criticisms of mine are purely on the level of physics, and are about MWI failing to satisfy the minimal standards that must be met in order to have a theory at all.
What do you mean by the technical challenge posed by relativity? As far as I can tell relativistic quantum mechanics is unusually satisfactory and uncontroversial.
In relativistic QFT, you start with something that is formally Lorentz-invariant (a Lagrangian density) and you end up with predictions that are invariant (or covariant), but to get from the Lagrangian to the predictions, you utilize objects and procedures which are frame-dependent and usually gauge-dependent too. Many basic properties of QFTs are still unproven (inconsistency of QED at Landau scale, existence of mass gap in QCD), and the theories have a somewhat heuristic existence, as an open-ended set of approximations and calculational procedures.
From an instrumentalist perspective, such procedures are relativistic if they start relativistic and end relativistic, with any frame-fixing and gauge-fixing that you do along the way “cancelling out” by the time you get to the end. But wavefunction realism is about reifying some of the objects which you use in the middle of that process, and they will usually bear the imprint of a preferred frame and a preferred gauge. Some of those objects are invariant or covariant (Heisenberg-picture operators, the S-matrix, asymptotic field states, some Feynman diagrams), but I sure don’t see how to turn them into the basis of an ontologically relativistic wavefunction realism, which is what relativistic MWI would have to be.
If all the rules governing the wavefunction are relativistic, then the result is relativistic. You can look at it however you like, including non-relativistic ways. I don’t see a problem here.
A lot of the time, the rules aren’t relativistic, just the input and output. MWI is a theory about what’s inside the black box of reality: wavefunctions! Wavefunctions are what’s real, it says. But the wavefunctions that actually get used in QFT are defined on a preferred time-slicing (closed time-path formalism), or they only exist asymptotically, in the infinite past or future (S-matrix)… The mathematical manipulations in QFT can be quite baroque, and I am very far from seeing how you could make them all relativistic at every stage.
The only way I can see to do it, is to break the theory down to the level of individual space-time points, allow continua of duplicates of points, define the analogue of Lorentz transformations in the resulting infinite-dimensional space, and then define a way to build the configurations (that enter into a wavefunctional in the position basis) out of these points, while also associating amplitudes or proto-amplitudes with the way that the points are glued together, so that configurations can have global amplitudes attached to them as required. It would be a sort of bottom-up approach to the “spacetime state realism” described by Wallace and Timpson, and it might not even be a well-defined approach for a QFT that isn’t UV-complete, like QED.
That was all a mouthful to say, and I regret introducing such complexity into the discussion, but that is how I think when I ask myself “how could you describe a quantum multiverse that is genuinely relativistic?” To ontologically ground QFT, you have to specify what it is that exists in the ontology, and you have to explain what the QFT calculational procedures mean ontologically—why they work, what real things they refer to. And if you’re going to ground it all in wavefunctions, and you don’t want to be stuck in a preferred frame, then you have to do something drastic.
When you describe a state, you need to choose a method of describing it, yes. But you can choose to describe it in any frame you like, and you can transform from one such description to another in a different frame. This is an artifact of the descriptions, not the thing in itself.
Like, you have a covariant quantity. You can do all sorts of symbolic math with it and it’s totally relativistic. But then you want to do a calculation. You’re going to have to pick a frame so you can work with actual numbers. These numbers are not vectors or tensors—they’re scalars. They themselves do not obey the transformation laws of the entities they represent.
BUT that doesn’t mean that using your description involves invoking a preferred frame. You know how to turn that description into a description in any other frame you like, and if you do, the results come out the same.
So, the time-slicing method is perfectly legit. In principle, you could use any mutually-time-like-separated slice, but it’s usually inconvenient to do so. (edit: I meant, ‘you could use any arbitrary mutually-SPACE-like-separated curve, but it’s usually inconvenient to pick anything more complicated than strictly necessary’)
I’ve made a sketch to illustrate the simplest version of the problem.
Horizontal direction is spacelike, vertical direction is timelike. On the left we have a classically relativistic theory. Everything reduces to properties localized at individual space-time points (the blue dots), so there’s no significance to a change of slicing (black vs pink), you’re just grouping and re-grouping the dots differently.
On the right we have a quantum theory. There’s a quantum state on each slice. A red circle around two dots indicates entanglement. How can we apply relativity here? Well, we can represent the same slicing differently in two coordinate systems, changing the space-time “tilt” of the slices (this is what I’ve illustrated). But if you adopt a truly different slicing, one that cuts across the original slicing (as pink cuts across black on the far left), you don’t have a recipe for specifying what the quantum states on the new slices should be; because the quantum states on the original slicing do not decompose into properties located solely at single space-time points. The entanglement is made up of properties depending on two or more locations at once.
In practical QFT, the situation isn’t usually this straightforward. E.g. perturbation theory is often introduced by talking about pure momentum states which notionally fill the whole of space-time, and not just a single slice. The Feynman diagrams which add up to give S-matrix elements then appear to represent space-time networks of point interactions between completely delocalized objects. I think it’s just incredibly un-obvious how to turn that into a clear wavefunction-is-real ontology. What’s the master wavefunction containing all the diagrammatic processes? What space is it defined over? Does this master wavefunction have a representation in terms of an instantaneous wavefunction on slicings that evolves over time? If it does, how do you change slicings? If it doesn’t, what’s the relation between the whole (master wavefunction) and the parts (history-superpositions as summed up in a Feynman diagram)?
And even that is all still rather elementary compared to the full complexity of what people do in QFT. So how to define relativistic MWI is a major challenge. I hope that the “simplest version of the problem”, that I started with, conveys some of why this is so.
Entanglement is over mutually-timelike regions, not merely simultaneous moments, so your diagrams are misleading. Try redrawing your ellipses of entanglement so they’re legal spacetime entities. If you redraw ALL of the entanglement this way, then it will transform just fine.
Entangled regions should be spacelike-separated from each other; do you mean that each individual region will have some internal timelike extension? Is this about the smearing of field operators to create normalizable states?
Maybe we should have this discussion privately. I’m quite keen to discuss technicalities but I don’t want to spam the site with it.
I misused a phrasing there—mutually timelike regions can only be 1 dimensional or less, just as mutually spacelike regions can only be 3 or fewer dimensional.
Entanglement is between points that are spacelike separated, but the boundaries of this entanglement—the processes that create or destroy it—are purely causal and local.
We can continue in PM. I just wanted to clear that up, since I ended on something that was flat-out wrong.
The Quantum Mechanics sequence is a failure—but fixing the physics is not the solution.
The point of the quantum mechanics sequence was the contrast between Rationality and Empiricism. Eliezer argues that the rational response to uncertainty when empirical evidence is absent or equipoise is to assign higher probability to the simpler explanation. But by writing at least 2⁄3 of the text about quantum mechanics, Eliezer obscured this point in order to pick an unnecessary fight about the proper interpretation of particular experimental results in physics.
Even now, it is unclear whether he won that fight, and that counts as a failure because MWI vs. Copenhagen was supposed to be a case study of the larger point about the advantages of Rationality over Empiricism, not the main thing to be debated.
Schoolkids often learn about this with Ptolemy vs Copernicus, I believe. It’s a much less confusing example.
I think the subtext: was: even professional physicists don’t get it.
Edit: Based on the responses, it appears I have confused Copernicus and Kepler pretty badly.
To the extent that “Copernicus is better than Ptolemy” does not pay rent in anticipated experience, I stand by my position that rationalists have no reason to assess the probability that the sentence is true.
Can you expand further? Because my impression was that “Copernicus is better than Ptolemy” pays rent pretty much immediately. Ptolemy can only keep up when there are no new observations. But the moment new observations occur, Copernicus says “Oval shaped orbits,” while Ptolemy needs to explain why it never noticed the need for another epicycle.
In short, the need to avoid privileging the hypothesis is distinct from the possible desirability of simpler theories. Or as Karl Popper might say, “Falsifiability, baby.”
Never. Orbits were circles for him. He “only” put the Sun in the center.
That sounds like the “epicycles on epicycles” fallacy.
It’s circles all the way down!
There’s a lot wrong with this. Timtyler below pointed one serious issue out. but also ellipses were not used by Copernicus but only later by Kepler. Copernicus has epicycles just like Ptolemy. Moreover it doesn’t pay rent immediately at all (either Kepler or Copernicus). Kepler’s work only paid rent because he had access to Tycho’s extremely precise observations over the course of many years. There are ways that Kepler’s system pays rent also that Ptolemy can’t at all, such as the transit of Venus across the sun but that only happens twice every hundred years. To a naive observer, or even to a naked eye astronomer, all three give pretty decent predictions over the course of a few decades.
Tycho was a naked eye astronomer. No telescopes, just money and awesomeness.
Yes he did naked eye astronomy but with a level of accuracy, precision and regularity not rivaled by any prior individuals.
Ignoring for the moment my huge confusion between Copernicus and Kepler, I don’t see why I care that naive observers can’t tell the difference between Kepler and Ptolemy—just like I don’t care that a naive observer can’t tell the difference between Newton and Einstein.
It is possible that I interpreted “Because my impression was that “Copernicus is better than Ptolemy” pays rent pretty much immediately” badly but I guess I didn’t see months of observation using telescopes would be what I would normally call “pretty much immediately” then. But this may be just an issue of timespan and equipment that is called to mind for “immediate”.
Exactly, that’s not what this post was about. But I did want to present concrete evidence that the central argument is flawed.
I’m not sure that the project is worth the effort, since it seems clear to me that the whole QM sequence contradicts the central point of “Making Beliefs Pay Rent.”
Even assuming all the physics in the QM sequence were perfect, I see no value comparing MWI to Copenhagen unless the difference matters somehow. That is, if the sentence “MWI is less wrong than Copenhagen” does not pay rent in anticipated experience, I’m unconvinced it is rational to have an opinion about the probability of that sentence. And if the sentence does pay rent in anticipated experience, why are we even thinking about which theory is more complex?
Until that issue can be resolved, searching for a particular scientific dispute to use as a case study is putting the cart before the horse.
MWI does make empirical predictions. E.g.: ‘No Collapse interpretation will be empirically supported.’ Thus far this prediction has been vindicated, even though Collapse interpretations, as a group, are verifiable. Of course, MWI has to share this glory with other alternatives to Collapse; but that’s at best a reason to dismiss arguments between MWI and Bohmian Mechanics, not a reason to dismiss arguments between MWI and Collapse.
As for Heisenberg-style Copenhagenists… if you think it makes no difference whether we accept or deny their view, then it would seem most consistent to also consider it a matter of indifference whether we affirm, deny, or remain agnostic regarding the doctrine of Solipsism. And I don’t think that’s tenable; our experiences provide experiential evidence against the supposition that there’s no reality transcending our immediate experience.
And assigns higher probability to an explanation that has not even been demonstrated sufficient to make predictions with (i.e. which, as far as we know, is ‘too simple’)
Really? I would pledge nonzero money towards this goal.
If it doesn’t happen in canon, I wouldn’t mind collaborating on a QM rationalist fanfic.
Feel free to elaborate.
Tim Maudlin developed an ingenious objection to the transactional interpretation which, to my knowledge, has not been adequately resolved as of yet. According to the TI, offer waves are sent forward in time from particle sources to absorbers. Each absorber responds by sending a confirmation wave backwards in time to the source. One of these transactions is selected with a probability given by the amplitude of the confirmation wave.
Here’s Maudlin’s objection: Suppose we have a beam splitter that can splits incoming beams of particles along two paths, call them a and b. On path a, at a distance l from the splitter, is a detector A. Let us suppose that a particle would cover the distance l in time t. There is another detector B that is initially also on path a, at a distance 2l from the source, behind A. If the detector A does not detect a particle within time t of the start of the experiment, then the detector B automatically swings onto path b, where it will also be at a distance 2l from the splitter.
Let’s say the beam splitter sends half of the particles along path a and half along path b. This means that, for an individual particle, ordinary quantum mechanics predicts it will be detected by detector A with probability 1⁄2 (in which case B won’t swing over to the other path), and with probability 1⁄2 B will swing over to path b and the particle will be detected at B. If the TI is to replicate these probabilities, then the confirmation waves sent backwards to the source from detectors A and B must have equal amplitude. But remember, a confirmation wave is sent back from an absorber only if an offer wave hits the absorber. So a confirmation wave will be sent backwards from detector B only if the offer wave from the source can reach B. But this is only possible if B has swung onto path b (otherwise the offer wave would be blocked by A), which in turn will only happen if the particle is not detected at A.
So if a confirmation wave is returned from detector B, then the particle must be detected at B. But if the QM probabilities are to be recovered according to the TI formulation, this confirmation wave’s amplitude must be 1⁄2, since detections at B only occur half of the time. So the recipe for recovering probabilities in TI is incoherent. The confirmation wave returned from B both guarantees that the particle is detected at B and sets the probability of the particle being detected at B as 1⁄2. There have been a number of attempts to deal with this problem in the literature, but I haven’t come across a wholly satisfactory attempt yet. The Wikipedia article on TI lists four articles that purportedly deal with this objection. I’ve read all of them, and don’t think any of the proposed resolutions work.
If I’m understanding this correctly, this implies that TI needs a “transaction eater” analogous to the “world eater” in the Collapse theory. This seems to be a liability of TI that isn’t matched by any liability of MWI.
But I’d never heard of TI before this post, so I could easily be missing something.
Yeah, it does require something like that. Proponents of the TI claim that ultimately every interpretation that actually accounts for the success of the Born rule will have to include some such component, and so MWI advocates are deluding themselves if they think they can avoid it.
There is a version of the TI (called the possibilist TI), where transactions aren’t actually “eaten”, in the sense that all possible transaction really occur in some possible world (and these possible worlds are real, they exist). But only one of these transaction occurs in the actual world. As for how to make sense of this, your guess is as good as mine.
That sounds like it’s simply MWI all over again.
As for accounting for the Born Rule - if the wavefunction is real, then any minds it implements, in any way, will have associated subjective experience. Among the minds implemented by the wavefunction are ours, and ours happen to be those that are associated to the wavefunction by applying the Born Rule.
It’s not, as far as I can tell. Proponents of the TI (and the PTI) explicitly say that one advantage of their interpretation over the MWI is that it is a one-world theory, because only one world is actualized. Spacetime is treated as fundamental, rather than emergent (as it would be in non-relativistic MWI, at least). I think there are aspects of MWI and TI that are vaguely specified enough that it might end up being the case that one can be translated into the other, but I don’t think this is obvious.
This approach seems inadequate. Part of our evidence for the truth of QM is that we get experimental results in line with the Born rule. In order for this to actually count as evidence, we need to show that QM is the sort of theory that should lead us to expect these relative frequencies. Simply saying, “Well, in MWI observers will see all sorts of different frequencies in experimental results, including Born-rule compliant ones” doesn’t tell us why observers should expect to see Born-rule compliant frequencies in a QM-governed world. And if you don’t have a story about that, then I don’t see how you can claim that the observed frequencies confirm QM (and by extension MWI).
Even the PTI? With the given description, that’s really really weird.
Not ALL sorts of frequencies. Many—most—ways of looking at the wavefunction won’t reveal causal structures isomorphic to observers. For instance, you can consider the wavefunction in the energy basis and interpret it as an infinite number of wheels of various sizes, spinning at different constant speeds. No observers are apparent when viewed this way.
I suspect that the Born Rule is the only rule that leads to observers, but we don’t need to prove that it’s the only one, and I’m open to the possibility that there are others. GAZP again—if it’s in there, it’s in there, whether or not you’re aware of it.
I think you’ll agree that the observed frequencies confirm the conjunction of Schrodinger’s Equation with the Born Rule. The question at hand is whether the Born Rule needs to be a rule of the universe. Whether collapse is ontologically real or based solely on our parochial viewpoint as observers.
Suppose it is real. That’s nice. We get everything we see.
Suppose it isn’t, and collapse isn’t a real thing. The wavefunction is just doing its thing, and that’s all there is. The causal structures in the wavefunction that correspond to people are still there.
The way of looking at us that brings us into focus is the Born Rule. Removing the Born Rule is just like removing a P-zombie’s consciousness. It’s that switch you flip to grant or remove subjective experience from a computation that implements consciousness.
Weird, but true! See the discussion of PTI in the paper I link to in this comment. As far as I can tell, PTI is just a relabeling of the original TI. Where TI would have said only one branch is real and the other branches do not exist, PTI says only one branch is actual and the others are real but not actual. Our universe consists only of that which is actual, so the other branches are not part of our universe. They exist in other possible universes, which (and this is the innovation, I take it) happen to be real. I don’t see how merely renaming the selection procedure from “collapse” to “actualization” helps, but I will admit to not having read that much about the PTI.
I’m reminded of David Lewis’s response to Armstrong’s theory of laws of nature. According to Armstrong, two properties are associated in a law-like manner if and only if there is a specific second-order relation that holds between them. Armstrong labels this relation the “necessitation relation” and claims to have thereby accounted for the ineluctable character of the laws. Lewis responds: “I say that [Armstrong’s ‘necessitation relation’] deserves the name of ‘necessitation’ only if, somehow, it really can enter into the requisite necessary connections. It can’t enter into them just by bearing a name, any more than one can have mighty biceps just by being called ‘Armstrong.’”
This is actually a tricky claim to adjudicate from the perspective of MWI. It’s certainly true that the relative frequencies of experimental results in our world support the Born rule. But why should the reference class be restricted to our world? For someone who has seriously absorbed MWI, this is akin to declaring that you only care about the frequencies of experimental results in North America. If you include all experimental results in your reference class, including those from other worlds, it is no longer the case that they confirm the Born rule unless you already assign weights to worlds based on the Born rule. But of course, assigning weights to worlds in this way would be question-begging if you were trying to provide evidence for the Born rule itself.
To put it another way, as a proponent of the MWI you believe that there are real scientists out there, in other branches of the wave function, who perform their experiments with just as much care and diligence as you do and who end up with wholly different observed frequencies within their world. What makes you think you have the right frequencies and they don’t?
You have completely missed my point. It’s the difference between, on the one hand: proving that there is life on Earth, and on the other proving that if there is life in the universe, it must be on Earth.
actual = the branch we’re observing.
real = part of the wavefunction of the universe.
I maintain my position that it’s the same thing as MWI.
Please clarify the question. Do you identify these scientists using the Born Rule to interpret the wavefunction so as to provide the basis for their consciousness, and making them just really unlucky in the outcomes? Because in that case, for every one of them, there are sixty gazillion jillion squillion ridiculillion others that get the same frequencies we get. This is very unlucky for them. Prospectively, we could expect their frequencies to fall in line immediately (and of course we can also expect that a vanishingly small measure of them will continue to fail to do so).
OR, are you finding these scientists out there in the wavefunction without using the Born Rule to interpret the wavefunction when identifying their consciousness, but using some other rule instead? If so, then the Born Rule isn’t right for them.
Following that logic why not go even further and remove Schrodinger’s Equation? All possible observer moments exist, we just happen to be observers whose history happens to correspond to the conjunction of Schrodinger’s Equation with the Born Rule.
That notion doesn’t bother me in the least, but if we’re talking about the physics that happen for us, it’s the Schrodinger Equation, and the Born Rule is the ‘angle’ to take on finding us in it. Anything else isn’t us, and we can’t do experiments on it, so we ought to avoid making strong claims.
Then I don’t understand on what grounds you reject the Born Rule but keep the Schrodinger Equation.
Because the Schrodinger Equation governs the absolute dynamics.
Let me draw an analogy to what things would be like if the world weren’t quantum.
Schrodinger Equation + form of the Hamiltonian : Born Rule + neuroscience
::
Newton’s 2nd Law + force rules : “Some of those masses are what we’re made of..” + neuroscience
Isn’t this sort of like the Tegmark multiverse?
I agree, more or less. For me, TI is significant as the best-known recent attempt to explain QM with retrocausality. But it has several concrete problems and this is one of them. When I liken the status of retrocausal interpretations to that of many-worlds, I have this in mind too.
I’m curious about the following...
Would John Cramer’s transactional interpretation require more complexity (at the level of the fundamental laws, rather than the amount of stuff in the universe) than the many worlds interpretation?
Roughly what proportion of the physics community backs it?
Is it a non-differentiable (or even discontinuous) phenomenon?
Is it non-local in the configuration space?
Does it violate CPT symmetry?
Does it violate Liouville’s Theorem (has a many-to-one mapping from initial conditions to outcomes)?
Is it acausal / non-deterministic / inherently random?
Is it non-local in spacetime?
Could it propagate an influence faster than light?
Can it represent a non-linear or non-unitary evolution?
No God-damned puppies were harmed in the making of this comment.
Edit: As pointed out, one of those things is not like the others, so to carve at the joints, let’s call the questions after #2 “the antimagic questions”, and the idea that we should reject the suggested interpretation if we get “yes” answers to them the cuddly collapsing canine conjecture.
This paper might be of interest to you:
Why Everettians Should Appreciate the Transactional Interpretation
Abstract: The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like “beginner’s mind” in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant (“PTI”), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don’t), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don’t bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010).
After some previous disappointments, my probability that this paper answers “No” to the above questions is too small to try to read yet another one. The more so as the author is obviously taking as burdens things that physics clearly permits, like bifurcating minds (which can be done with uploads on computers, never mind MWI). Have you read it and can you confirm a “No” to all the antimagic questions?
Yeah, I don’t think this paper is going to convert you. As my other comment on this thread will attest, I consider TI pretty much a failed project, so maybe I’m not the best person to defend it. Still, here’s my most charitable attempt to answer MichaelHoward’s questions on behalf of TI.
TI has a claim to be less complex than MWI in one respect. Relativistic versions of the Schrodinger equation have both advanced (waves propagating backwards in time) and retarded (waves propagating forward in time) solutions. A relativistic version of MWI would presumably ignore the advanced solutions by fiat (or based on some “principle of causality”, which I think just amounts to fiat). Specifying this condition adds to the complexity of the theory. TI doesn’t require this specification, since the interpretation incorporates both advanced and retarded solutions. Another advantage of TI is that it does not require specification of a preferred basis.
What about MWI’s main claim to simplicity, the lack of any collapse postulate or hidden variables? The original TI involved the “selection” of one transaction out of many in accord with the Born rule, and this might be regarded as tantamount to collapse. A new version of the TI developed by Ruth Kastner (called the PTI, or possibilist transactional interpretation), defended in the linked paper, goes modal realist, and declares that all possible transactions are real, but only one is actual. I don’t know what to make of this claim. I don’t understand how “actualization” is any better than “collapse”. Simply declaring the other branches to be real doesn’t help if you still need to appeal to a mysterious selection procedure, even if the selection procedure only determines what is actual rather than what is real. Perhaps it is possible to make sense of actualization in a non-mysterious manner, separating it from collapse, but I haven’t seen evidence of this. The paper says at one point, “Such actualized transactions will furthermore naturally line up with decoherence arguments, since decoherence… is fundamentally based on the nature of absorbers available to emitted particles.” I don’t understand this claim.
Of course, Cramer and Kastner claim that MWI’s advantage in this regard is illusory, a product of disregarding the Born rule. Any attempt to account for the full formalism of quantum theory (unitary evolution + the Born rule) will have to involve some component like their actualization procedure. This ignores Deutsch and Wallace’s attempts to ground the Born rule in assumptions about rational decision-making, which I think are promising (although I know you, Eliezer, disagree).
A very very small proportion, I’m fairly sure.
All of this depends on how you interpret the “actualization” step in the PTI account. I take it that it’s not meant to be a dynamical process like objective collapse, in which case the dynamics have a claim to being continuous, time-reversible, unitary, etc. I should note that thinking of a retro-causal interpretation in terms of our usual dynamical systems framework (talking about the “evolution of the quantum state”, for instance), can be misleading. These theories explicitly reject the idea that explanatory priority implies temporal priority.
Well, depends on what you mean. Influence transmission is restricted within light cones, but since this transmission can be either backwards or forwards in time, you can get phenomena which, from a temporally chauvinistic point of view, appear to involve FTL transmission.
Neither the many-worlds interpretation, nor any retrocausal interpretation, has a canonical, ontologically satisfactory, self-contained definition as a theory. In both cases, you will find people who say that the interpretation is just a way of thinking about quantum mechanics, so the calculational procedure is exactly the same as Copenhagen.
If you dig a little deeper, you can find quantum formalisms which are self-contained algorithmically, and which possess some resemblance to the spirit of the interpretations, such as consistent histories (for many worlds) and two-state-vector formalism (for single-world retrocausality). I can’t say that one of these is clearly simpler than the other.
By the way, Eliezer’s original argument for simplicity of MWI has the following flaw. The comparison is between Everett and Collapse, and we are told Collapse has two axiomatic forms of dynamics—unitary evolution and collapse—where Everett just has one—unitary evolution. But then we learn that we don’t know how to derive the Born rule from unitary evolution alone. So to actually use the “theory”, you have to bring back collapse anyway, as a separate part of your calculational algorithm!
Retrocausality is a minority preference compared to many worlds, there’s no doubt about that. It could be like 1% versus 20%. If you also counted people who are just interested by it, you should add a few more percent.
It is meant to be relativistically local and that takes care of the majority of those questions. Whether it is non-differentiable or non-deterministic would depend on the details of a proper retrocausal theory. For example, Wheeler-Feynman theory is just classical electrodynamics with waves that converge on a point as well as waves that spread from a point, whereas the two-state-vector formalism is stochastic.
One of those questions is not like the others, but I’d also like to hear an answer to all the others. Obviously, if even one answer is “Yes”, then I will instantly toss it out the window unless it has an experimental consequence different from MWI or a strictly endogenous answer to the Born rule. (“We use the Born rule to decide which world survives!” is not endogenous, it is pasting an arbitrary mechanism attached to the same rule-of-unknown-origin treated as fiat.) If there are two “Yes” answers that aren’t the same “Yes”, I will toss it even if it has endogenous Born. Any damn idiot can introduce a bunch of magic and sneak in some fairly arbitrary linkage to measure which eventually yields the Born probabilities—I’d expect thousands of theories like that, and I’d expect none of them to be right. The great achievement would be getting Born without magic, where ‘magic’ is represented by a “Yes” to any of the above questions.
What do you think about Relational QM? That’s where I’d put most of the single-world, comprehensible-to-this-layman probability. It doesn’t seem to require faster-than-light influence on a real particle or any obvious non-locality.
RQM as an alternative to MWI seems to just assert that if we take correlations as fundamental, we find that only one history holds together logically. I do not expect this to hold, because if it did then I’d need a reason not to expect a proof that MWI is impossible. But perhaps if I understood the topic better I would find it unfair to demand such a proof.
The framework of Wheeler-Feynman theory is just classical Maxwell electrodynamics with waves that converge on a charged particle as well as waves that spread from a charged particle. So it ought to be just as relativistic and local and deterministic as it usually is, except that now you’re interested in solutions that have two oppositely directed arrows of time, rather than just one. (Remember that the equations themselves are time-symmetric, so “emission” of radiation can, in principle, run in either direction.)
In practice, they artificially hacked with the theory to remove self-interactions of particles (particle absorbing its own emissions at a later or earlier time), because that produced incalculable infinite forces; but then they were unable to account for the Lamb shift, which does come from self-interaction; and then somehow Feynman made the leap to path integrals, and in the quantum framework they could deal with the infinities of self-interaction through renormalization.
It may seem like a big leap from the classical to the quantum picture. But classical dynamics can be expressed as wave motion in configuration space via the Hamilton-Jacobi equation, and it’s not a big step from the HJE to quantum mechanics. Also, doing anything practical with path integrals usually involves working with classical solutions to the equation of motion, which in the quantum theory have high amplitude, and then looking at corrections which come from neighboring histories.
It’s quite conceivable that these quantum deviations from classicality may result from the interference of forward causality and retrocausality. Maybe the Wheeler-Feynman theory just needs some extra ingredient, like micro time loops from general relativity, in order to become consistent. We would be dealing with a single-world model which is locally causal but not globally causal, in the sense that the future would also be shaped by the distribution of micro time loops, and that’s not determined by its current state. Our world would be one of an ensemble of self-contained, globally consistent “classical” histories, and the quantum probability calculus (including the Born rule) would just turn out to be how to do probability theory in a world where influences come from the future as well as from the past. For example, the Aharanov “two-state-vector formalism” might show up as the way to do statistical mechanics if you know yourself to be living in such an ensemble. There would be no ontological superpositions. Wavefunctions would just be “probability distributions with a future component”.
The status of these speculations is remarkably similar to the status of many worlds. The construction of an exact theory along these lines, with a clear explanation of how it connects to reality, remains elusive, but you can assemble suggestive facts from the quantum formalism to make it plausible, and there is a long tradition of people trying to make it work, one way or another: Wheeler and Feynman, John Cramer, Yakir Aharonov.
Practical QM contains the dualism of wavefunctions and classical observables. Many worlds reifies just the wavefunction and tries to find the observables in it. Retrocausality just keeps the classical part and tries to explain the wavefunction as something to do with forwards and backwards causality. Bohmian mechanics keeps the wavefunction and then fleshes out the classical part in a way governed by the wavefunction. Nomological Bohmian mechanics keeps the classical part of Bohmian mechanics, and replaces the wavefunction with an additional nonlocal potential in the classical equations of motion. If you could obtain that nonlocal potential from a local retrocausal theory, you would finally have an exact, single-world, deterministic explanation of quantum mechanics.
It’s worth noting that most of these are strawmen put up by Yudkowsky, not actual properties of non-Everett interpretations.
( self citation )
Which ones are not actual properties of the collapse interpretation?
I don’t think Eliezer has suggested they were properties of all possible non-Everett interpretations.
Did you read the post I linked?
He certainly doesn’t seem to address anything but Everett and objective collapse (which he also appear to conflate with Copenhagen).
That later edit wasn’t in the comment when I read it. Thanks for adding.
Personally, I am against linking MWI or even QM to rationality in any way, as the connection seems to be quite arbitrary.
Consider a matrix-like world, where the Universe is simulated on a classical computer (classical computers can do everything quantum computers can do, if slower). Would you deny that simulated humans can think and act rationally, only because the simulation does not include quantum mechanics? If not, would sim-EY not be able to write the Simquences (less the QM Sequence) which are identical (modulo QM) to the ones here?
You make a compelling case that the reference to QM in the sequences is at least as arbitrary as the fundamental physics of our universe. I’m not sure that this is quite as compelling and incisive a revelation as you believe it to be, especially to those who take Occam’s Razor as seriously as Eliezer advocates. I’d actually say that this weakens your claim and that it would be better to argue, as Tim does, that the points Eliezer is trying to express don’t come across nearly as well as they could.
It seems to me like the universe could be simulated on a quantum computer without quantum mechanics in the simulation, or even in a classical computer with quantum mechanics in the simulation (though it’d take a lot longer of course). The information processing itself is the important part, not the means of processing. This doesn’t detract from your argument, which I agree with, I just wanted to point that out.
Right, I just wanted to underscore that no QM is required at any point (the point I mentioned before, but it never got any attention from EY).
The first question—there’s no reason in the QM sequence to suspect that simulated humans would not be able to think or act rationally. The phenomenon of rationality is well-screened from the implementation layer of the universe.
Sim-EY would be correct about that implementation layer of his universe that screens off all the lower levels. That is, his statements about the universe are true of the simulation, which, as far as he can tell, is all there is. His words have valid referents. And indeed, MWI would be correct in that domain.
That there is another implementation layer out there that isn’t quantum… eh so? We’re perfectly screened from it, so that’s not what we’re talking about.
My point exactly, QM (and hence the QM sequence) is not needed for rationality training.
You lost me with the last statement. MWI would be correct in what domain? The simulated one? Hardly, it’s all classical and digital.
Total non-sequitur. The QM sequence was a case study. You don’t need to understand QM to be rational, but to get where he was going, he needed to use something as an example.
The implementation of the simulation is classical digital. The simulated world is quantum, just like you said.
Ah, I see. Yes, it was a case study, just not a good one, given the controversy that distracts from the point. There are better examples.
I don’t follow. What’s the difference between the implementation and the simulated world?
In two simulations I ran once, the ‘world’, such as it was, was an FCC lattice each containing one of 2 kinds of atom, or vacuum, and the dynamics were ruled by a Monte Carlo algorithm.
It had two separate implementations, with very different MC engines. One was in Fortran77 and used the Metropolis algorithm; another was in C++ and used the Bortz-Kalos-Lebowitz MC algorithm. Both of these had effects on how dynamics progressed. They would be detectable by examination of the state of the world.
But which computer I chose to run it on would not. I put it on a Solaris machine; I put it on a Linux machine. the results were bitwise identical.
If you scale this notion up into the point that it could contain agents, and let these two swap save-files every so often, an agent inside could in principle tell which program was running at that time. But no agent could tell whether I’d changed from a Solaris box to a Linux box. So, the Metropolis vs BKL distinction is an element of their physics. The Solaris vs Linux distinction is not.
Accordingly, if we’re in a simulation, and the simulation is pure quantum, but it’s implemented in classical computers, it’s not wrong to say MWI is correct. The referent is the implementation of quantum mechanics in those classical computers.
OK, I think I understand and mostly agree. Though I would make a weaker, interpretation-agnostic statement: “it’s not wrong to say QM is correct”. I don’t think that it invalidates my original point, however, that it is likely possible to simulate human-like agents discussing rationality using, say, Newtonian physics, and such agents will have no need for QM.
Well, yes, but I don’t see how that has anything to do with the QM sequence.
Again, my (and others’) long-standing point has been that the QM sequence as a case study is not a good one. Given that the same rationality-related arguments can likely be made in a world without QM, and that the MWI discussion sparks too much controversy that detracts from the point (whatever it might be), it stands to reason that a different case study would serve this goal better (it can hardly be worse).
If the case-study pertained to banana custard stands, certainly rationality-related arguments would be devisable in a world without banana custard stands.
That aside—MWI being controversial is a fair point, which is why I didn’t have anything to say about it in the post with the simulation analogy. I suppose I should have explicitly acknowledged that then, so you would not feel the need to raise it again. Sorry about that.
BTW, I hope you are not the one who immediately downvotes almost all my QM-related posts.
I am not. I have a batch of −1 posts elsewhere on this page myself, and I trust you’re not behind them.
edit: oh come ON. How could this get upvoted? sheesh people. Maybe this could have been done in PM, but if it should have, then nail us both for it.
Just checked… No, not a single one is mine, though I did upvote a couple earler.
Voted Up for precision disagreement.
Pros for Down: Claiming error on chain of reasoning without pointing the flawed link, treating a sequence as community manifesto instead of Elizers stance
Pros for Up: Topic that allows education of audience (QM), focused and individualized disagreement. introducing of a subfield of theory, voiced dissent
In favour of this de-bugging. One of the other glaring omissions from the sequence is discussion of modal interpretations of quantum mechanics. These are formally very similar to MWI (there is a wave function for the universe, there is no collapse) but the “many worlds” are interpreted as possible worlds (or universes), only one of which is actual. This approach has a lot going for it, common-sense wise.
Modalism has its place in a discussion of the options. But in fact my call for “debugging” was not aimed at reforming the account of QM provided by the Sequence. The arguments about QM serve to illustrate various general points—e.g. “think like reality”—and I’m saying that a functional substitute for all that should be constructed, or at least outlined. We should at least have an idea of what could take the Sequence’s place in the flow of argument, if one were to remove it.
Some thoughts on modal interpretations:
The concept of a modal interpretation is even vaguer in its implications than many-worlds and retrocausal interpretations. The only unifying concept seems to be that other worlds exist in the discourse, but they are purely counterfactual and play no role in explaining anything that happens in the one actual world.
There are various theorems (“Hardy theorems”) proving that an ontological theory can’t assign definite values to all observables in all quantum states, such that all QM expectations are satisfied simultaneously. “Antirealists” like to use this as evidence that you can’t make an objective theory that accounts for QM. But you never perform all possible measurements simultaneously; all that matters is that what the theory says about position when position is measured matches what QM says, and the same for other observables. At other times, position can be doing whatever is required by the logic of the new theory, it can even be absent ontologically.
The modalists have brought all this to the fore and they even have a few technical insights about the construction of a full proper theory, but so far as I can see, these insights aren’t comprehensive enough to single out an ontologically distinctive class of theory, compared to many-worlds or retrocausality. Bohmian mechanics, especially in its wavefunction-less “nomological” form, is a modal interpretation in the sense that, e.g. Bohmian momentum behaves like quantum momentum only when a momentum measurement is occurring. (The Bohmian mechanics of the measurement interaction forces it to behave appropriately.)
You could even argue that many worlds is modal! - in the technical sense that a “world” or “branch” which is an eigenstate of some observable will not provide an associated eigenvalue for a complementary observable.
I don’t agree that the concept of a modal interpretation is vague. The basic concept is that a quantum system can have a physical property with a definite value without its wavefunction necessarily having to be in an eigenstate of the corresponding operator. So the eigenstate-eigenvalue link is not bidirectional. That’s basically it.
The only vagueness is that there are then multiple interpretations, each of which assigns different properties as the ones which have the definite values. So which properties does the system have then, and how can we tell?
I think you mean Kochen-Specker theorem here (and similar results going back to Gleason’s theorem)? The system can’t have definite (non-contextual) values of all operators at once, because the operators don’t commute. Particular interpretations build a maximal set of properties which the system can have at once. Hardy’s theorem seems to be related to whether the properties can be Lorentz invariant or not.
As you say, Bohmian mechanics is one of the interpretations (based on assigning definite position states to all particles at all times), but perhaps is not the most plausible one, since the choice of the position operator as the “preferred” operator is “put in” by hand. Other interpretations try to allow the preferred operators to “drop out” of the wave function (via measurement events or other decoherence events) rather than being “put in” and are in that sense simpler (fewer assumptions) and more plausible.
You seem then to be left with the problem that the “real” world can be affected by the “imaginary” ones, otherwise you don’t get interference. The sense in which this makes sense does not seem to me to be ‘common’.
Did you read the link? Most of the recent modal interpretations are based heavily on decoherence (between different branches of the wave function). So, no, the possible worlds don’t “interfere” with each other.
There are different ways of splitting the wave function into “worlds”—this is why there are several modal interpretations, not just one of them. This ambiguity is a more powerful criticism by the way (exactly what are the worlds, and why should we believe one particular split rather than the others?)
In any case, I think you missed the point here. Whether the modal interpretations are right or not, the problem is that they are just not discussed in the sequence. Instead, the sequence contains a colossal non-sequitur from “wave function collapse is a silly theory” to “so all these many worlds really exist”.
Did we independently develop this “MWI and transactional interpretation are on roughly equal footing” rhetorical move? Just curious.
I was saying they were tied for (lack of) clarity three years ago.
Ah, I must have seen that. Non-disjunctive then. Thanks.
This whole post seems to be a conjecture about what quantum mechanics really means.
What we know about quantum mechanics is summed up in the equations. Interpretations of quantum mechanics aren’t arguing about the equations, or the predictions of the equations. They are arguing about what it means that these equations give these predictions.
The important thing here is to understand what exactly these interpretations of quantum mechanics are talking about. They aren’t talking about the scientific predictions, as all the interpretations are of the same equations, and necessarily predict the same behaviour. By the same token they aren’t talking about anything we might see in the universe, as all the various interpretations predict the same observations.
Now sometimes people do propose new theories about the quantum world that lead to different predictions. These aren’t interpretations of quantum mechanics, they are new theories. Interpretations are attempts to talk about the current standard theory in the most helpful way.
As far as I can tell, creators of interpretations are looking at the elephant which is quantum mechanics, and discussing whether all angles from which to observe the elephant are equally good, whether some are better than others, or whether only the view we can actually see ourselves is the only one that truly exists.
Now it is useful to try and find new ways of looking at the elephant, as maybe some views are better than others, and someday we might have data that moves us to a new theory where viewpoints that seem equally good now are shown not to be. But right now there isn’t any such information, and so we can’t really say that one view is better than another. Saying that one answer is better than another, in the absence of relevant information, doesn’t seem helpful.
That’s the basis on which we prefer many worlds (all outcomes allowed by the equations exist) to collapse (there is only the outcome I can see). It’s part of the general principle of not making up complicated explanations on matters where evidence is lacking.
After some confusion about what you are trying to say, I’ll just point out that you use “views” to first mean different interpretations, and then different worlds within the one interpretation, so I give up.
Thanks—I’ve amended the final paragraph to change ‘view’ to ‘outcome’ throughout—hope it helps.
From what I can remember, part of the sequence explains correctly what predictions QM makes and part of it boldly asserts that MWI is the only reasonable interpretation. The former part is a fairly standard introductory text, it’s the latter which makes the sequence unique, and the role of the “MWI is the winner” seems to be pretty central there. But I’d need to read the thing again to have a clearer idea. So, do you think it’s worth the time to read (again) through the whole QM sequence to find the exact role of the declaration of MWI’s superiority there?
Hello, I’m posting this because I saw some earlier comments about PTI that needed correcting.
PTI does not have ‘world branches’ like MWI. If you read the material at the end of my FoP article (http://arxiv.org/abs/1204.5227)
and my new book, http://www.cambridge.org/us/knowledge/discountpromotion/?site_locale=en_US&code=L2TIQM
Chapters 3 and 6 in particular, you will see that there is already a ‘transaction eater’ in PTI (if I understood that notion correctly); i.e., something that really does result in ‘collapse’. These are the absorbers, properly understood (and I give a precise definition of what an ‘absorber’ is.) PTI was developed to better define ‘absorber,’ to extend TI to the relativistic domain, and to address the fact that multiparticle q. states are 3N-dimensional, too ‘big’ to fit into spacetime. So I view them as physical but sub-empirical possibilities—something ‘more real than ideas’ but ‘less real than things of the facts’, as Heisenberg first suggested.
So the possibilities in PTI are not ‘other worlds’ containing sets of macroscopic object including observers. Rather, each possibilitiy is just a possibility for a transaction resulting in a single spacetime event. The set of spacetime events that we experience as our macroscopic world are the actualized transactions corresponding to specific individual events. So this is definitely not just another version of MWI. Thank you for your interest in TI and PTI. Best wishes, RK
I have a problem with your Possibilist TI that I also had with original TI, and with almost every ontological interpretation except for Bohmian mechanics—I can’t figure out what the ontology is; nor even what the mathematical object is, that represents reality in the theory.
If Einstein had had his way, reality would have been described by classical fields on a manifold. Mathematically the universe would be represented by some particular exact solution of the equations of motion. Even given that, we could still ask the ontological questions like, what is a property, what is a causal relation and why does it necessitate anything, and so on; but at least the mathematics would be clear.
Quantum mechanics also has a certain clarity, if you resolutely regard it as not ontological, but just as an algorithm for making predictions. The observables are what’s real, but they are an incomplete description of reality, and wavefunctions etc are a recipe for making predictions, whose reasons for working are unknown and remain to be discovered.
A peculiar laxity regarding the notion of reality, and regarding what counts as an adequate specification of an ontological theory, entered physics when people started trying to regard quantum mechanics as a complete theory of reality, rather than an incomplete one; and many ontological interpretations have inherited some of these lax attitudes, even as they try to restore objectivity to physical ontology. At least, this is how I explain to myself the oddities that I keep encountering in the literature on quantum foundations.
I will give another example of an ontological interpretation whose mathematical basis I think is clear—and it’s a “back-and-forth-in-time” theory like TI: Mark Hadley’s idea that QM arises from subatomic time loops. Hadley’s ontology is like Einstein’s, fields on a manifold, but the difference is that the manifold is non-orientable, it’s full of little time loops, and quantum mechanics is supposed to arise from the global consistency constraints imposed by the coexistence of innumerable coexisting causal loops. The idea may or may not work, but at least the mathematical starting point is clear.
One more example of non-clarity before I turn to TI: MWI. MWI says that reality consists of one big wavefunction or state vector—OK, that much is clear. The non-clarity in this case comes when you ask, what parts of the wavefunction or state vector correspond to observable reality? Are the “worlds” the components of the wavefunction, when decomposed in a special basis? Or do all possible basis decompositions produce another, equally real set of worlds? Etc., lots of questions which have been raised many times on this site.
Now to TI. Let me give an example of an ontological claim that might have been made about TI, which would have provided a clear starting point. It could have been claimed that what exists are particles and fields. The particles trace out world-lines, the fields do their thing. And then the TI claim could have been, that the fields can be decomposed, in some specific way, into a particular set of advanced waves and retarded waves, which can be arranged into the “pseudo-time sequence” making up a “transaction”.
That sounds like a clear starting point to me. And then the challenge would be to go into the details—describe how the decomposition works, and explain why the quantum formalism is the appropriate and correct way to compute probabilities in this world where influences are going back and forth in time “simultaneously”.
That is not what I found in John Cramer. Instead, his only visible mathematical foundation is just, the usual quantum formalism. Then he has a few specific physical setups, where he tries to communicate the gist of the TI way of thinking. Also, as I recall, there is a path integral formalism in which advanced and retarded waves appear.
At this point, as a “philosophy of QM”, TI appears structurally very similar to CI. The math is still just the same quantum formalism, perhaps amended to include advanced waves in the path integral. There is no clear mathematical description of the ontological part of the theory. Instead, there is just a way of thinking and a way of talking about the traditional quantum formalism. In CI, it’s Bohr going on about complementarity and the uncertainty principle, in TI, it’s Cramer going on about pseudotime sequences.
I have not yet seen your book, but so far, I don’t find, in Possibilist TI, an improvement on this situation. Instead, there seems to be just an extra layer to the talking, in which “possibilities” are ascribed an important role. It’s a little odd that something nonexistent should matter so much for the understanding of that which exists, but I can let that go, it’s not my main concern. My main concern is just—what is the mathematical object, that corresponds to reality? I’ve already given two examples of theories where there is no mystery at all about what that is—fields on a manifold, and fields on a nonorientable manifold. I’ve also given a clear example of a theory that does not attempt to be ontologically complete, namely, QM with observables regarded as real, and wavefunctions regarded as not real.
What I would like to know is just, what sort of mathematical object describes the actual part of Possibilist TI ontology? Is it a definite history of particles and fields, which then gets ontologically analyzed in a certain way (and perhaps that is where the “possibilities” come in)? If I open your arxiv paper, I see kets, propagators, quantum fields, squared amplitudes, and a whole pile of stuff which just looks like standard quantum formalism. So it looks like you have produced just another way of talking about the quantum formalism, rather than a clear ontology whose objects can be specified with mathematical exactness. Please prove me wrong, and show me the part where you just say “These are the entities that exist, and these are the states they can have.” :-)
I address this question of ontology in my book, and I strongly suggest you take a look at that. (I know the book is a bit pricey, but you can always get it from a library! ;)
But here’s a reply in a nutshell.
First, the whole point of PTI is the idea that QM describes REAL possibilitites that do not live in spacetime—i.e., that spacetime is not ‘all there is’. So the QM objects DO exist, in my interpretation. That’s the basic ontology. The mathematical object that describes these real possibilitites is Hilbert space. Again: ‘what exists’ is not the same as ‘what is in spacetime’. Not being in spacetime does not disqualify an entity from existing. This is where I think ‘mainstream’ attempts to interpret QM stumble, because they automatically assume that because the quantum state (or ‘wavefunction’) does not live in spacetime, it therefore necessarily describes something that ‘doesn’t physically exist’, i.e., it only describes knowledge. I think that’s a false choice. Remember that it was Heisenberg who first suggested that QM states describe a previously unsuspected kind of physical reality. That’s the idea I’m pursuing.
There are no ‘particles’ in TI or PTI. So at a basic level, it is interacting field currents that are fundamental. These are the physical possibilitites.
As for the actual events, these comprise a discretized spacetime corresponding to the transactions that have been actualized. This is a definite history of energy exchanges between emitters and absorbers, and is the emergent ‘classical’ world. I invite you to Chapter 8 of my book for further details. A specific example of the emergence of a ‘classical’ trajectory is given at the end of Chapter 4.
Again, the main point: ‘physically real’ is not equivalent to ‘existing in spacetime’. Quantum states describe physically real possibilitites that do not live in spacetime, but have their existence in a realm mathematically described by Hilbert (actually Fock) space. Spacetime is just the set of actualized events—i.e. emitters and absorbers that have exchanged energy via actualized transactions.Each of these defines an invariant spacetime interval. But note that this is a relational view of spacetime—the latter is not a substantive, independently existing structure. It’s just a map we use to describe the set of actualized events.
To address your final question directly: the things that can be actualized are described by the weighted projection operators in the von Neumann mixed state ([process 1′) occurring on measurement—the weights are just the Born Rule. (TI is the only interpretation that can physically explain this ‘measurement’ transformation.) The thing that is actualized is described by the projection operator ‘left standing’ while the other ones have disappeared. These are ‘just’ properties, if you like, but they are supported (as a substratum) by the emitter and absorber involved in their actualization. So in PTI, the spacetime arena of phenomena, i.e., observed properties, is rooted in a pre-spacetime substratum of physical possibilitites.
After some puzzlement (because it is so unlike what I expected), I think I now understand your interpretation. Possibilist TI is essentially a growing block universe which consists of a set of state vectors with a timelike partial order (a little like this), and the growth is a stochastic feeling out of immediate future extensions of this poset, via potential transactions.
For various reasons I can’t believe in that as a final ontology, but I can imagine that it would have heuristic value, and maybe even practical value, for people trying to understand the nature of time and causal dependency in a universe containing backward as well as forward causality.
Thanks Mitchell—it’s only at the nonrelativistic limit that there is a timelike partial ordering in this sense, and that emerges stochastically from the relativistic level. I.e., there is no temporal causal relationship in the basic field propagation. So my picture isn’t quite captured by the formulation in this paper (which also doesn’t appear to address wf collapse and the possible relation of collapse to an emergent spacetime). But in any case, thanks again for your interest and I hope you will take a look at the book. The main dividend you get from the TI picture is a robust solution to the measurement problem, in contrast to the ‘FAPP’ quasi-solution obtainable from decoherence approaches. In particular, decoherence never gives true irreversibility, since you never get real collapse with decoherence alone. In PTI you get true collapse, which also sheds light on macroscopic irreversibilty. I discuss this in my book as well.
Too much digital ink has already been spilled over this word “obvious”; I suggest we await the revised sequence and see whether or not EY will stick by “obvious” there before returning to the point at hand.
Probably because there is no precise definition of “obvious”? Does it mean “trivial”, as in “its proof requires the skills much lower than those expected from the audience”? Clearly (ehm) not, since no interpretation can be proved or disproved. Does it mean “inevitable”, as in “it can be proven from the premises, given some effort”? Nope, not that, either. So, no point arguing over whether MWI is obvious until everyone agrees what “obvious” means and how to check for obviousness.
If not everyone can agree on what “obvious” means then it is wrong to use the word in an argument.
Obviously.
I agree wholeheartedly.
What “revised sequence”?
In the wonderful shiny future when the sequences are finally compiled into something.
Eliezer won’t be rewriting anything for the Sequences ebook. It’ll just be typo corrections and link fixes and stuff, done by not-Eliezer.
I thought the sequences ebook market was already flooded with fanworks. Or are you not trying to turn a profit on it?
I’m curious about the following...
Would John Cramer’s transactional interpretation require more complexity (at the level of the fundamental laws, rather than the amount of stuff in the universe) than the many worlds interpretation?
Roughly what proportion of the physics community backs it?
Is it a non-differentiable (or even discontinuous) phenomenon?
Is it non-local in the configuration space?
Does it violates CPT symmetry?
Does it violate Liouville’s Theorem (has a many-to-one mapping from initial conditions to outcomes)?
Is it acausal / non-deterministic / inherently random?
Is it non-local in spacetime?
Could it propagate an influence faster than light?
Can it represent a non-linear or non-unitary evolution?
No God-damned puppies were harmed in the making of this comment.
I’m not sure what you are exactly proposing with your suggestion to “patch the argument”. Here is my understanding (possibly incorrect, I’ve not been here for long) of what happened:
Yudkowsky claims to have found a practically usable method of inductive inference that is superior to the mainstream scientific method. In order to demonstrate it, he picks an area where mainstream scientific epistemology failed to yield conclusive and satisfactiory results: the interpretation of quantum mechanics.
Armed with his superior epistemology, he sets forward to shine the light of reason on the darkness of chaos and confusion and… fails spectacularly.
So what do you make of it?
1) Yudkowsky’s epistemology is not as good as he claims
2) The issue is very technical and Yudkowsky’s lack of domain expertise prevents him from making an informed contribution
3) Both
If you pick 1) then you may want to “patch” the epistemology, but that doesn’t seem an easy task. In fact, it would be far from obvious that it could be even patched rather than just be discarded as a failed attempt.
If you pick 2) then you may want to “patch” the domain expertise and see whether the Yudkowskian epistemology leads to a better result, but that requires said epistemology to be defined well enough that it can be uncontroversially applied by people who are not Yudkowsky.
If you pick 3) then, well, good luck.
Actually, I just want to patch the overall flow of argument in the Sequences.
I think we all agree that some form of Occam’s razor makes sense, and that it can become a quantifiable criterion if you pose it in terms of “how many bits does it take to specify this hypothesis as a predictive algorithm?”
But I don’t agree that Everett versus Collapse is a very good illustration of the razor, because you have to smuggle collapse back into MWI as a calculational ansatz (Born rule) in order to make it predictively useful. So I count this as one example of how the overall structure of the Sequences calls for a particular argument or case study, but the QM Sequence doesn’t really deliver, so a substitute example should be found.
Yes.
That’s a much stronger claim:
It’s unclear whether this is the proper way of formalizing Occam’s razor.
Even if it was, it is an uncomputable approach, and, as far as I know, there aren’t even reasonably methods to approximate it in the general case.
It’s uncomputable if you want to compare all possible hypotheses according to this criterion, but not if you just want to distinguish between hypotheses that are already available and fully specified. Also, it doesn’t have to be the way to formalize the razor, to have some validity.
This assumes that you can computably map each hypothesis to a single program (or a set of programs where you can computably identify the shortest element).
For arbitrary hypotheses, this is impossible due to the Rice’s theorem.
If you write your hypotheses as prepositions in a formal language, then by restricting the language you can get decidability at the expense of expressive power. The typical examples are the static type systems of many popular programming languages (though notably not C++).
Even then, you run into complexity issues: for instance, type checking is NP-complete in C#, and I conjecture that the problem of finding the shortest C# program that satisfies some type-checkable property is NP-hard. (the obvious brute-force way of doing it is to enumerate programs in order of increasing length and check them until you find one that passes).
You don’t smuggle it in as an ansatz.
You apply the generalized anti-zombie principle. There was a reason he went there first.
But that just tells you that other branches are conscious too. It doesn’t give you the Born rule. So it is an ansatz, it’s a guess about what formula to use. And until you can derive it from the unitary evolution rule, it counts separately towards the complexity of your model.
If you get as far as allowing that the other branches are conscious—no, simply that you even HAVE branches, and they should be related by probabilities that don’t change retroactively—then you have been granted sufficient grounds to derive the Born Rule.
It’s getting that far that’s the hard part.
EDIT: I’ve provided this derivation already, here Does that help?
This is too harsh. Yudkowsky’s conclusions aren’t that far from the positions of many mainstream specialists. The main problem with the sequence is, as Mitchell_Porter has noted, its overconfidence and insistence on obvious superiority of MWI. But that is a rather subtle mistake; calling it a spectacular failure would be needless exaggeration.
Also, I think the E.Y.’s epistemology is sound (and not that exotic; most components have been around for decades at least) and his expertise (or lack thereof) may have caused him to overlook some existing alternatives to MWI but wasn’t the main problem. To me it seems as if the epistemology endorsed elsewhere in the sequences was misapplied; instead of explaining away the question about the real essence of apparent collapse in a similar way as he has explained away the questions about the essences of sound or free will, he insisted on a verbal explanation of dubious meaning just because he found it unimaginable to have the concept of wave function not refer directly to an element of objective reality.
The position of mainstream specialists is that MWI is plausible, but there is no compelling evidence or theoretical arguments to conclusively decide in favour of one particular interpretation, and they have personal preferences largely based on intuitive appeal. Others go further and claim that the whole QM interpretation issue is meaningless and scientifically improper.
Therefore, there is no consensus on the issue in the mainstream scientific community.
Yudkowsky attempted to resolve the issue once and for all, and I think it’s uncontroversial to say that he objectively failed.
Most of its elements (empiricism, bayesian inference, etc.) are sound and essentially uncontroversial. Some elements specific to his version (“informal” Solomonoff Induction and Kolmogorov complexity) are more questionable.
Science google off, Bayes googles back on. If that is the state of affairs in science, then we know MWI is the better one because it is simpler.
Sorry, this statement is inconsistent with the other paragraph I quoted above. Either the scientists are undecided because there’s no evidence, and Occam clear it up as EY says, or the scientists are in some other state and the whole sequence is built on bad premises.
Unless you literally mean “once and for all”, which isn’t what he attempted to do, and is a strawman. (He said given the current state of evidence, we must prefer MWI to Collapse, and that there should be no controversy about this, not that MWI was 100% correct and will never be replaced.)
The goal of the sequence is to convince us of this position. But if we hypothesize that the difference between the two theories does not pay rent in anticipated experience, then I’m unconvinced that it is rational to say that one theory has higher probability—certainly not to the level of certainty presented in the sequence.
If one wants to argue that research resources are poorly allocated between less complex and more complex hypothesis, have at it. I don’t disagree, but I think re-engineering the practice of scientific research is sociology issue, not a pure right and wrong issue.
Even granting the assertion that one should assign probability to beliefs that don’t pay rent, it really requires a specialist to determine that MWI is the simpler explanation. Eliezer’s ridicule of the collapse theories could fulfill that function, but my sense is that his talented-layperson perspective leads him astray. Much like the difference between “clear and present danger” and “imminent lawless action” are hard to distinguish unless one has studied the relevant free speech law.
And that’s why quantum mechanics was a poor choice of topic for the case study. Eliezer doesn’t know enough physics to justify his confidence in the relative simplicity of MWI. And fighting that fight is totally distinct from the essential issue I discussed above.
If I offered two competing theories:
Each electron contains inside it a tiny little angel that is happy when things go well in the world and sad when things go badly. But there’s absolutely no way to detect such from the outside.
Electrons don’t actually contain any entities with minds inside them, even undetectable ones.
I think you’d assign higher probability to the latter theory, even though there’s no difference in anticipated experience between the two of them.
As I mentioned before, whether MWI is better or not, the QM Sequence itself is based on too controversial an example, and so failed to achieve the desired educational effect (whatever that might be, I am not sure, something Occam-related, apparently). I am hard-pressed to believe that there is not a single other example in all of physics which would illustrate the same point with less controversy.
Good point. I don’t disagree with that.
You’re a physicist, do you know of any better examples of issues where traditional science googles and bayes goggles disagree?
By the very nature of the topic, any contemporary examples cannot fail to be controversial. If “traditional” scientific rationality supports position X, then many or most scientists will support X, and the claim that they are wrong and the true position is the Bayes-supported Y is bound to be controversial.
So for non-controversial examples one would have to look to the history of science. For example, there must have been cases where a new theory was proposed that was much better than the current ones by Bayes, but which was not accepted by the scientific community until confirmed by experiments. Maybe general relativity?
Physicists love simplicity, so they are naturally Bayesian. Unfortunately, Nature is not, otherwise the cosmological constant would be zero, speed of light would be infinite, neutrino would be massless and the Standard Model of Particle Physics would be based on something like SU(5) instead of the SU(3)xSU(2)xU(1).
until general relativy was confirmed by experiments, who besides einstien had the necessary evidence? I’m not familiar with the case enough to really say how much of a difference there should have been.
To me Bayes is but one calculational tool, a way to build better models (i.e. those with higher predictive power), so I do not understand how Bayes can disagree with the traditional scientific method (not the strawmanned version EY likes to destroy). Again, I might be completely off, feel free to suggest what I missed.
Bayes is the well proven (to my knowledge) framework in which you should handle learning from evidence. All the other tools can be understood in how they derive from or contradict Bayes, like how engines can be understood in terms of thermodynamics.
If you let science define itself as rationality (exactly what works for epistemology), then there can be no conflict with Bayesian rationality, but I don’t think current (or traditional, ideal) science is constructed that way. Some elements of Eliezer’s straw science are definitely out there, and I’ve seen some of it first hand. On the other hand, I don’t know the science scene well enough to find good examples, which is why I asked.
Bayesian updating is a good thing to do when there is no conclusive evidence to discriminate between models and you must decide what to do next. It should be taught to scientists, engineers, economists, lawyers and programmers as the best tool available when deciding under uncertainty. I don’t see how it can be pushed any farther than that, into the realm of determining what is.
There are plenty of Bayesian examples this crowd can benefit from, such as “My code is misbehaving, what’s the best way to find the bug?”, but, unfortunately, EY does not seem to want to settle for a small fry like that.
Likewise with conclusive evidence. Bayes is always right.
I think I’ve confused you, sorry. I don’t mean to claim that Bayes implies or is able to support realism any better or worse than anything else. Bayes allocates anticipation between hypotheses. The what-is thing is orthogonal and (I’m coming to agree with you) probably useless.
1: It’s an overkill in this case.
2: If you are doing science and not, say, criminal law, at some point you have to get that conclusive evidence (or at least as conclusive as it gets, like the recent Higgs confirmation). Bayes is still probably, on average, the fastest way to get there, though.
Feel free to unpack what you mean by right. Even your best Bayesian guess can turn out to be wrong.
So? It’s correct. Maybe you use some quick approximation, but it’s not like doing the right thing is inherently more costly.
This get-better-evidence thing would also be recommended by bayes+decision theory. (and if it wasn’t then it would have to defer to bayes+decision). Don’t see the relevence.
The right probability distribution is the one that maximizes the expected utility of an expected utility maximizer using that probability distribution. That’s missing a bunch of hairy stuff involving where to get the outer probability distribution, but I hope you get the point.
You can often get lucky by not using Bayesian updating. After all, that’s how science has been done for ages. What matters in the end is the superior explanatory and predictive power of the model, not how likely, simple or cute it is.
So, on average, you make better decisions. I agree with that much. As I said, a nice useful tool. You can still lose even if you use it (“but I was doing everything right”—Bayesian’s famous last words), while someone who never heard of Bayes can win (and does, every 6⁄49 draw).
It’s “gotten lucky” exactly to the extent that it follows Bayes.
Yes. cuteness is overridden by evidence, but there is a definite trend in physics and elsewhere that the best models have often been quite cute in a certain sense, so we can use that cuteness as a proxy for “probably right”.
Yes, a useful tool, but also the proven most-optimal and fully general tool. You can still lose, but any other system will cause you to still lose even more.
I think we are in agreement for the most part. I’m out.
EDIT: also, you should come to more meetups.
Thursday is a bad day for me...
I think you are missing the point.
It’s unclear whether MWI is the simplest interpretation. If it was, it would have been uncontroversially accepted. Occam’s razor is a core principle of the standard scientific method.